Roditty and Vassilevska W. [1]}, following Aingworth, Chekuri, Indyk and Motwani [2]}, designed a \(3/2\) -approximation algorithm running in \(\tilde{O}(m\sqrt{n})\)  time, for the case when the diameter is divisible by 3, and with an additional small additive error if it is not divisible by 3. Chechik, Larkin, Roditty, Schoenebeck, Tarjan and Vassilevska W. [3]} gave a variant of the algorithm that runs in \(\tilde{O}(m^{3/2})\)  time and always achieves a \(3/2\) -approximation (with no additive error). These algorithms work for directed or undirected graphs with nonnegative edge weights.
